Best Known (74, 90, s)-Nets in Base 5
(74, 90, 9769)-Net over F5 — Constructive and digital
Digital (74, 90, 9769)-net over F5, using
- net defined by OOA [i] based on linear OOA(590, 9769, F5, 16, 16) (dual of [(9769, 16), 156214, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(590, 78152, F5, 16) (dual of [78152, 78062, 17]-code), using
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- OA 8-folding and stacking [i] based on linear OA(590, 78152, F5, 16) (dual of [78152, 78062, 17]-code), using
(74, 90, 41952)-Net over F5 — Digital
Digital (74, 90, 41952)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(590, 41952, F5, 16) (dual of [41952, 41862, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(590, 78152, F5, 16) (dual of [78152, 78062, 17]-code), using
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(590, 78152, F5, 16) (dual of [78152, 78062, 17]-code), using
(74, 90, large)-Net in Base 5 — Upper bound on s
There is no (74, 90, large)-net in base 5, because
- 14 times m-reduction [i] would yield (74, 76, large)-net in base 5, but